1. The problem statement, all variables and given/known data Given f(x) = -x2 - 2x + 3, x < -1 Find f-1. Find f-1f. 2. Relevant equations Nil. 3. The attempt at a solution Actually I worked out much of the question already, and I already know that f-1f: x -> x. The problem is, I can't seem to get f-1f(x) = x on substitution. Here goes: Let y = -x2 - 2x + 3 4 - y = (x+1)2 x = - 1 +/- sqrt(4-y) Since the domain of f is the range of f-1, we have f-1: x -> -1 - sqrt(4-x), x < 4 Consider f-1(x) = -1 - sqrt(4-x) Substituting f(x), f-1(f(x)) = -1 - sqrt(x2+2x+1) = -x-2 OK, here's the problem. I know I will get f-1f(x)= x if sqrt(x2+2x+1) = -x-1 and I understand that x2+2x+1 = (x+1)2 = (-x-1)2 but my reasoning here doesn't reject -x-2 as a valid answer. Where is the mistake in my working?